*Hybrid Modeling Procedure of Li-Ion Battery Modules for Reproducing Wide Frequency… DOI: http://dx.doi.org/10.5772/intechopen.88718*

data acquisition systems (in the case of electric applications). To perform the HIL simulation of the battery-pack, the experimental setup shown in [26] is used. In this test bench, the load regime is simulated by means of a MATLAB/Simulink model (software simulation). This current signal is used to control (by DSpace control system) the output signal of an electronic load and a power source connected in parallel to reproduce the charging/discharging cycles. This configuration is called hardware simulation; in this way, real devices are used to test the battery-pack. A control schema of the HIL simulation is shown in **Figures 8** and **9** that presents a picture of the test bench.

Three simulations of the battery-pack performance under dynamic regimes associated with distribution grids operation have been analyzed. The first one corresponds to a load frequency control application (LFC), which is related to grid frequency control, with typical time constants ranging from 0.2 ms to 10 s. The second one reproduces the dynamic voltage support (DVS) of a renewable energy source during 110 s. The simulated models of these load regimes are based on the operation of a hybrid ac/dc microgrid presented in [29]. Finally, the third one simulates the performance of an energy support device uninterruptible power supply (UPS). The time duration of this energy support is less than 30 min; and to

**Figure 8.** *HIL simulation control setup.*

*Research Trends and Challenges in Smart Grids*

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**Figure 7.**

**Table 3.**

*Battery-pack impedance parameters.*

*Battery-pack model.*

where:

network, respectively:

*uc2*, and *uc3* simulate the voltage response of the ohmic resistance and each *RC*

− *uC*1(*SOC*,*t*) − *uC*2(*SOC*,*t*) − *uC*3(*SOC*,*t*) (2)

**Element 20% SOC 40% SOC 60% SOC 80% SOC 90% SOC** *Ro (Ω)* 0.039 0.039 0.039 0.039 0.039 *τ1(C1//R1) (s)* 23.40 18.43 15.71 11.39 10.92 *τ2(C2//R2) (s)* 0.295 0.188 0.136 0.116 0.106 *τ3(C3//R3) (s)* 0.0028 0.0030 0.0030 0.0029 0.0028

*uRo*(*SOC*,*t*) = *Ro*(*SOC*) ∙ *ipack*(*t*) (3)

*uC*1 \_ (*SOC*) *R*1(*SOC*) 

*uC*2 \_ (*SOC*) *R*2(*SOC*) 

*uC*3 \_ (*SOC*) *R*3(*SOC*) 

) ∙ *dt* (4)

) ∙ *dt* (5)

) ∙ *dt* (6)

*upack*(*SOC*,*t*) = *Eo*(*SOC*,*t*) − *uRo*(*SOC*,*t*)

\_1

*C*1(*SOC*)

\_1

*C*2(*SOC*)

\_1

*C*3(*SOC*)

∙

∙

∙

To verify the accuracy and reliability of the proposed model to simulate the battery-pack behavior, hardware-in-the-loop simulations are used. HIL is a widely used experimental technique to reproduce the real conditions of physical applications [27, 28], using lab devices such as electronic loads, power sources, sensors, and

(*ipack*(*t*) <sup>−</sup>

(*ipack*(*t*) <sup>−</sup>

(*ipack*(*t*) <sup>−</sup>

*uC*1(*SOC*,*t*) = ∫

*uC*2(*SOC*,*t*) = ∫

*uC*3(*SOC*,*t*) = ∫

**3. Hybrid model validation**

**Figure 9.** *Test bench picture.*

test the transient response, different current steps have been simulated. The current profiles associated with these applications are shown in **Figures 10**–**12**. These current signals are used as the input signals of the HIL simulations. The simulations have been performed at different SOC values to check the model response under SOC variations. **Figures 13**–**18** present the comparison of the voltage response of the hybrid model (*Umodel*) and the voltage measurement at battery-pack terminals (*Ubpack*) during the HIL simulations.

**Figure 10.** *Current profile of LFC simulation.*

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**Figure 15.**

**Figure 13.**

**Figure 14.**

*Simulation results at LFC (48% SOC).*

*Simulation results at LFC (72% SOC).*

*Simulation results at DVS (45% SOC).*

*Hybrid Modeling Procedure of Li-Ion Battery Modules for Reproducing Wide Frequency…*

*DOI: http://dx.doi.org/10.5772/intechopen.88718*

**Figure 12.** *Current profile of UPS simulation.*

*Hybrid Modeling Procedure of Li-Ion Battery Modules for Reproducing Wide Frequency… DOI: http://dx.doi.org/10.5772/intechopen.88718*

#### **Figure 13.**

*Research Trends and Challenges in Smart Grids*

(*Ubpack*) during the HIL simulations.

test the transient response, different current steps have been simulated. The current profiles associated with these applications are shown in **Figures 10**–**12**. These current signals are used as the input signals of the HIL simulations. The simulations have been performed at different SOC values to check the model response under SOC variations. **Figures 13**–**18** present the comparison of the voltage response of the hybrid model (*Umodel*) and the voltage measurement at battery-pack terminals

**152**

**Figure 12.**

**Figure 11.**

**Figure 10.**

*Current profile of DVS simulation.*

*Current profile of LFC simulation.*

*Current profile of UPS simulation.*

*Simulation results at LFC (48% SOC).*

#### **Figure 14.**

*Simulation results at LFC (72% SOC).*

**Figure 15.** *Simulation results at DVS (45% SOC).*

**Figure 16.** *Simulation results at DVS (73% SOC).*

**Figure 17.** *Simulation results at UPS (53% SOC).*

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*Hybrid Modeling Procedure of Li-Ion Battery Modules for Reproducing Wide Frequency…*

simulation are 0.28% (LFC), 0.40% (DVS), and 0.23% (UPS).

The validations tests show that the hybrid model simulates the battery-pack behavior with high accuracy in all cases analyzed. The maximum errors for each

This chapter presents a hybrid modeling procedure of Li-ion battery-packs which is able to simulate the dynamic behavior associated with electric grid applications. The parameters of an electrical circuit have been calculated from experimental results of current interruption and EIS tests. The active behavior of the battery-pack has been simulated by a voltage source, and the impedance reflects the electrochemical processes by means of three *RC* networks (which correspond to three different time constants) and an ohmic resistance. The experimental procedure has been performed at the whole battery-pack in order to include the interac-

To reproduce the battery-pack behavior under high dynamic applications of distribution grids, a hardware-in-the-loop platform has been used. Three different cases (load frequency control, dynamic voltage support, and uninterruptible power supply) at different SOC conditions have been simulated. The validation results show that the hybrid model reproduces the dynamic behavior of the battery-pack

*DOI: http://dx.doi.org/10.5772/intechopen.88718*

tions of battery cells and BMS components.

with high accuracy in all cases analyzed.

The authors declare no conflict of interest.

**Conflict of interest**

**4. Conclusions**

**Figure 18.** *Simulation results at UPS (78% SOC).*

*Hybrid Modeling Procedure of Li-Ion Battery Modules for Reproducing Wide Frequency… DOI: http://dx.doi.org/10.5772/intechopen.88718*

The validations tests show that the hybrid model simulates the battery-pack behavior with high accuracy in all cases analyzed. The maximum errors for each simulation are 0.28% (LFC), 0.40% (DVS), and 0.23% (UPS).
